UC Berkeley

In the first part of this thesis, we study the non-parametric

methods for estimation and optimization. In particular, a new

non-parametric method, objective operational statistics, is proposed

to inventory control problems, where the only information available

is the sample data and we do not assume any relationship between

demands and order quantities. A kernel algorithm based on objective

operational statistics is constructed to approximate the objective

function directly from sample data. Moreover, we give conditions

under which the operational statistics approximation function

converges to the true objective. Numerical results of the algorithm

with applications to newsvendor problem show that the objective

operational statistics approach works well for small amount of data

and outperforms the previous parametric and non-parametric methods.

In the second part of this thesis, we present a robust hedging

problem under model uncertainty and the bounds of the optimal

objective value are derived by duality analysis.